I get the same "please enable cookies" response on my android tablet with ICS and Chrome. If I click a link from that page, it gives me an SSL certificate error, and if I tell it to proceed anyway, it finally loads the forums. Firefox on the same tablet goes straight to the forums, no muss and no fuss.
See if you can get the same from the Kindle's native Silk browser. If not, you might want to see if Amazon's app store has Opera or Chrome or Firefox available.
I don't plan to log into the forums from my tablet at all, so I haven't tested whether that works. (Retyping login information every hour is enough of a pain with a real keyboard; I'll pass on doing the same with a tablet keyboard.)
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